) Verify Stokes' Theorem for the hemisphere S : x²+y²+z² = 9, z > 0, %3D its bounding circle C: 1? +y = 9, z = 0, and the field F = y - x). %3D

Q: 2. Let vector field F=(xz,-y,z) and surface, S is a cylinder x+y = 4 for 3<z<0 with %3D outward…

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Q: Let F = 4ai + 1yj and let C be the closed path around the circle x² + y² = 9, traversed once…

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Q: Evaluate the surface integral [/ where F(x, y, z)= xi + yj + z²k and S is the surface parameterized…

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Q: Which of the space curves describes the vector-valued function r(t) = (t + 15, e0.08t cos(t), e0.08t…

A: Identify the graph of the vector function .From the equations it follows,,  and Now fix the value of…

Q: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on a…

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Q: xi + yj x2 + y2 F(x, y) = k-

A: Topic- vector integration

Q: 2. (b) Q 3 p sin фа, + p'zag +z cos ф a,

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Q: Verify the validity of the Stokes's theorem for the vector A = e-bz sin ø a, + pe-bz , over the open…

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Q: 6. Compute the Divergence and Curl of the following vector F:F = yze#vi + xze#¥j+(e™y + 3 cos 32)k…

A: Use divergence and curl formula Compare hyperbola with standard equation of hyperbola

Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: Prove the polarisation identity for the norm and dot product: for all x; y in R^n,

A: The polarization identity for the norm and dot product states that: ||x+y||2 + ||x-y||2 = 2||x||2 +…

Q: a) Find the unit tangent vector 7(1), unit normal vector Ñ(t), and unit binormal vector B(t) to the…

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Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: Let vector field F =(x,y,z²) across the surface S which is an upper hemisphere x²+ y² + z² = 4 . 1)…

A: Let vector field F =(x,y,z²) across the surface S which is an upper hemisphere x²+ y² + z² = 4 . 1)…

Q: Use Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7…

A: Stokes' Theorem: The formula for Stokes' Theorem is given by:         ∫CF→·dr=∬RCurl F→·n→ dA where…

Q: F. Sketch the region onto which the sector r ≤ 1,0 ≤ 0 ≤/4 is mapped by the transfor- mation (a) w =…

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Q: i) Calculate length of the curve r(t) = acost î+ asint ĵ+ 4t k from (a,0,0) to (a,0,87).

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

Q: Assume that the cylinder in Figure has equation x² + y² = r² and the plane has equation z = ax + by.…

A: To find the vector parametrization r(t) of the curve of intersection using the trigonometric…

Q: D) Evaluate f (r² + y²) dady where D is the disk z² + y² ≤ 4. Usc polar coordinates. (Ans: 647/5) E)…

A: To solve the following

Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: 1. Give the equation of any plane which is has a normal vector n = 2i- j + 3k.

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Q: 3. Verify Stokes' Theorem for the vector field F = 2zi +3xj+5yk , taking S to be portion of the…

A: We will use the basic knowledge of vector calculus to solve this question.

Q: Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate…

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Q: Given the vector field F, (a) determine the vector ₹ evaluated at P (r = 2,0 = 2,0 =,=); (b)…

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Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

Q: Name the transformation that maps figure T onto the correct T',T", T"" T" T' T T"" Drag the boxes to…

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Q: ff curl(x²yi - rzk). n do over the closed surface of the ellipsoid 4 16 Warning: Stokes' theorem…

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Q: b) Evaluate both sides of Stokes's theorem for the vector field B = r cos o î + sin o by evaluating…

A: Given the vector field is B=rcosϕr^+sinϕϕ^ and the given figure is

Q: Let F = . Use Stokes' Theorem to evaluate curlF rlFds, where S S is the hemisphere x² + y² + z² = 4,…

A: I have explained everything with in the solution, please go through that.

Q: b) The line integral F. dr is a scalar.

A: Check whether given statement is true or false.